League of Legends High Ping/500 Ping Disconnects

Hi,For a long time now, whenever I play the game League of Legends, the game tends to spike in ping between 300-1700, and even at some points to as high as 7000-9000. Most often it falls onto 500 ping which is when it 'attempts to reconnect' (making the game unplayable). This happens consistently throughout the game, reconnecting me and then disconnecting me (when it reconnects me, all I can do is watch the rest of the players doing things, I can't actually move my character as the game is still lagging so much). As my dad is the one who set up the broadband, he's been in the most contact with Plusnet as to what's going on, this is because when this happens (namely, whenever I play League) my internet drops too. When I used Skype, the call would drop or whoever I was on a call to could tell I was lagging by the interference in the call when I spoke, I recently begun using Curse Voice, but the same occurs (Curse actually shows you the ping, and it too reflects the spikes that I get when on League, though doesn't usually rise above 800). I've run numerous speedtests, and the results never seem to reflect what I'm experiencing, they often show 13-36 ping, 15mpbs, and a fine upload speed. I should note that this tends to most frequently occur between 11pm and 1am recently, and I don't think it's my PC as when I have friends over on their laptops, if we play league we all seem to disconnect at the same time, and any Skype or Curse call seems to drop too. I'm genuinely out of options as to how to resolve it, and I guess you understand the impact a player disconnecting from the game can have specifically in League of Legends (or any other MOBA). Hopefully someone can help me with this issue, Thanks!